Consider this graph:
From the definition, a perfect matching of a graph with $2n$ vertices is a subgraph consisting of $n$ disjoint edges.
The problems is I started counting them one by one and came across too many of them, thus doubted what I was doing. How do you count them? Any theorems? How many are there?
I see 5 subgraphs: {3 vertical edges}, {nw horizontal, se horizontal, sw-ne diagonal}, {ne horizontal, sw horizontal, nw-se diagonal}, {w vertical, ne horizontal, se horizontal}, {e vertical, nw horizontal, sw horizontal}